How do you solve x−3y=4 and −3x+5y=−14 using substitution?

1 Answer
Sarah C · Becca M.
Mar 20, 2016

y=0.5
x=5.5

Explanation:

First, we rearrange one of the formulae to give us x in terms of y (or vice versa)
x−3y=4 (Add 3y to both sides)
x=4+3y

Now we can substitute in our value for x into the other equation so that we only have one unknown, y.

Then you expand the bracket and simplify it to find y.

−3x+5y=−14
−3(4+3y)+5y=−14

(expand the brackets)

−12−9y+5y=−14

(simplify the y terms)

−12−4y=−14

(add 12 to both sides)

−4y=−2

(divide both sides by −4 to isolate the y term)

y=−2−4
y=0.5

We then substitute the y value into the original equation to find x (you can use either of the equations for this)

x=4+3y
x=4+(3×0.5)
x=4+1.5
x=5.5

Then we can use the other equation to check our answer.

−3x+5y=−14
−(3×5.5)+(5×0.5)=−14
−16.5+2.5=−14
−14=−14
So we know our answer is right!

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